C. Lutz and R. Moller. Defined topological relations in description logics. In M.-C. Rousset et al., editor, Proceedings of the International Workshop on Description Logics, DL'97, Sep. 27-29, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... calculus RCC 8 [26] have been proposed [7, 16] The addition of a concrete domain to a DL is a rather sensitive operation as far as the preservation of its nice computational properties is concerned: even weak DLs combined with weak concrete domains can become undecidable; see, e.g. [8, 15, 25]. In fact, to investigate DLs with concrete domains is rather hard and requires developing new techniques; cf. 24] ii) Standard DLs have been designed to represent static knowledge which is timeand agent independent. To take into account the dynamic aspects of knowledge, DLs have been extended ....

V. Haarslev, C. Lutz, and R. Moller. Defined topological relations in description logics. In Proceedings of the 6th International Conference on the Principles of Knowledge Representation and Reasoning (KR'98), pages 112--124, 1998.

....therefore unsatisfiable. This shows that special figure is indeed subsumed by figure touching a figure. Please note that there are also other description logics suitable for spatial reasoning tasks, namely the language ALCRP(D) see [11] However, unrestricted ALCRP(D) is undecidable (see [15]) and its decidable fragment suffers from very strong syntax restrictions, dramatically pruning the space of allowed concept expressions. In fact, the finite model property is ensured in restricted ALCRP(D) The strong syntactic requirements make modeling with ALCRP(D) much more complicated, ....

C. Lutz and R. Moller. Defined topological relations in description logics. In M.-C. Rousset et al., editor, Proceedings of the International Workshop on Description Logics, DL'97, Sep. 27-29, 1997, Gif sur Yvette, France, pages 15--19. Universite Paris-Sud, Paris, September 1997.

....(see also Figure 1) Thus, equal p 2 is subsumed by g inside p 5 . Grigni et al. have emphasized [ 4 ] that constraint systems that are (relationally) consistent must not necessarily lead to situation that are realizable in the plane. Thus, an additional planarity test must be added (see also [ 11 ] ) For other concept forming operators similar techniques can be applied. StructuralSubsumes [ # sr c) # sr 1 c1) # sr 2 c2) returns true i# c2 # c1 and # x, y, z # P : sr 1 (x, y)#sr 2 (x, z) is inconsistent. In order to compute whether a concept term based on the ....

....concrete predicates that depend on information available from attribute chains starting with this concept. Spatial relations cannot be adequately defined with the operators and primitive roles o#ered by ALC(D) Another solution might be the new role forming operator of ALCRP(D) as proposed in [ 11 ] . Then, the term (# sr c) could be replaced by (# sr(has area) has area) c) However, the satisfiability problem for ALCRP(D) has shown to be undecidable (see [ 11 ] Grigni et al. 4 ] study the computational problems in developing an inference system for checking the satisfiability of ....

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C. Lutz and R. Moller. Defined Topological Relations in Description Logics. In Proc. DL'97, 1997 International Workshop on Description Logics, September 27 - 29, 1997, Gif sur Yvette (Paris), France.

....term is All humans who are older than 60 years. The example demonstrates that defining concept terms (e.g. #age. 60 ) based on predicates over concrete objects (e.g. 60 ) greatly extends the expressiveness of the knowledge representation formalism. The language ALCRP(D) defined in [8] goes one step further. It also allows one to define roles based on predicates over concrete objects. Like in the ALC(D) example above, predicates over concrete objects that are attached to abstract objects via features can be seen as properties of these abstract objects. Take again humans and ....

....powerful language for reasoning about abstract and concrete knowledge. Like ALC(D) it can be parameterized with a concrete domain, which is a set of concrete objects plus a set of predicates over these concrete objects. Unfortunately, reasoning in ALCRP(D) is undecidable in general as proven in [8]. In [5] syntactic restrictions to be posed on ALCRP(D) terminologies are introduced. It is shown that w.r.t. these so called restricted terminologies sound and complete algorithms for deciding the common reasoning problems exist. Decidability is achieved by restricting the free combinability of ....

C. Lutz and R. M oller. Defined topological relations in description logics. In M.-C. Rousset et al., editor, Proceedings of the International Workshop on Description Logics, DL'97, Sep. 27-29, 1997, Gif sur Yvette, France, pages 15--19. Universite Paris-Sud, Paris, September 1997.

.... of Spatioterminological Reasoning with Description Logics Volker Haarslev, Carsten Lutz, Ralf Moller Computer Science Department University of Hamburg Vogt Kolln Str. 30 22527 Hamburg, Germany Abstract This paper presents a method for reasoning about spatial objects and their qualitative spatial relationships. In contrast to existing work, which mainly focusses on reasoning about qualitative spatial relations alone, we integrate quantitative and qualitative ....

....in order to ensure termination of the satisfiability algorithm, we impose restrictions on the syntactic form of the set of terminological axioms. Although modeling is harder, the restrictions on terminologies ensure decidability of the language. In contrast to our earlier work presented in [ 13 ] 10 ] and [ 14 ] where topological relations are used as primitives in the sense of logic, we extend the treatment of topological relations with respect to terminological reasoning. Thus, the theory presented in this paper allows one to detect both inconsistencies and implicit information in formal ....

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C. Lutz and R. Moller. Defined topological relations in description logics. In Rousset et al. [ 25 ] , pages 15--19.

....a TBox T i# it has a model w.r.t. T . The ABox consistency problem is to decide whether a given ABox A is consistent w.r.t. a TBox T . Satisfiability of concept terms can be reduced to ABox consistency as follows: A concept term C is satisfiable i# the ABox a : C is consistent. In [27], it was proved that reasoning with ALCRP(D) will be undecidable if the full expressive power is used. Therefore, in Section 2.3 syntactic restrictions on the concept language are introduced. But first, a remark about concrete domains is appropriate. 2.2 A Note on Concrete Domains In [5] it is ....

....Problem. From this it directly follows that the subsumption and ABox consistency problems are also undecidable. In fact, even for a logic comprised only of conjunction, value restriction, the top concept, and the role forming predicate operator, the standard reasoning problems are undecidable (see [27]) A more thorough analysis (see [27, 25] reveals that ALCRP(D) does have neither the finite model property nor the tree model property if instantiated with an appropriate concrete domain. 3 This does not imply, but is a strong indication for the undecidability of the formalism. And in fact, ....

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C. Lutz and R. Moller. Defined topological relations in description logics. In M.-C. Rousset et al., editor, Proceedings of the International Workshop on Description Logics, DL'97, Sep. 27-29, 1997, Gif sur Yvette, France, pages 15--19. Universite Paris-Sud, Paris, September 1997.

....human) The extension of the above mentioned concept term is All humans who are older than 60 years. The example demonstrates that defining concept terms based on predicates over concrete objects (e.g. 60 ) is a valuable tool for knowledge representation. The language ALCRP(D) defined in [Lutz and Moller 1997] goes one step further. It also allows one to define roles based on predicates over concrete objects. Like in the ALC(D) example above, these predicates over concrete objects that are attached to abstract objects via features can be seen as properties of these abstract objects. Take again humans ....

....language for reasoning about abstract and concrete knowledge. Like ALC(D) it can be parameterized with a concrete domain, which is a set of concrete objects plus a set of predicates over these concrete objects. Unfortunately, reasoning in ALCRP(D) is undecidable in general as proven in [Lutz and Moller 1997]. In this paper we propose syntactic restrictions to be posed on ALCRP(D) terminologies. We show that w.r.t. these so called restricted terminologies sound and complete algorithms for deciding the common reasoning problems exist. Decidability is achieved by restricting the free combinability of ....

[Article contains additional citation context not shown here]

Lutz, C. and R. Moller (1997, September). Defined topological relations in description logics. In M.-C. Rousset et al. (Ed.), Proceedings of the International Workshop on Description Logics, DL'97, Sep. 27-29, 1997, Gif sur Yvette, France, pp. 15--19. Universite Paris-Sud, Paris.

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C. Lutz and R. Moller. Defined topological relations in description logics. In M.-C. Rousset et al., editor, Proceedings of the International Workshop on Description Logics, DL'97, Sep. 27-29, 1997.

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